Properties

Label 3.3.1369.1-27.1-d
Base field 3.3.1369.1
Weight $[2, 2, 2]$
Level norm $27$
Level $[27, 3, 3]$
Dimension $3$
CM no
Base change yes

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Base field 3.3.1369.1

Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 12x - 11\); narrow class number \(1\) and class number \(1\).

Form

Weight: $[2, 2, 2]$
Level: $[27, 3, 3]$
Dimension: $3$
CM: no
Base change: yes
Newspace dimension: $47$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

\(x^{3} - 3x^{2} - 13x + 23\)

  Show full eigenvalues   Hide large eigenvalues

Norm Prime Eigenvalue
8 $[8, 2, 2]$ $\phantom{-}e$
11 $[11, 11, w]$ $-\frac{1}{4}e^{2} - \frac{1}{2}e + \frac{7}{4}$
11 $[11, 11, -w^{2} + 3w + 7]$ $-\frac{1}{4}e^{2} - \frac{1}{2}e + \frac{7}{4}$
11 $[11, 11, w^{2} - 2w - 8]$ $-\frac{1}{4}e^{2} - \frac{1}{2}e + \frac{7}{4}$
23 $[23, 23, w^{2} - 2w - 7]$ $\phantom{-}\frac{1}{2}e^{2} - \frac{1}{2}e - 5$
23 $[23, 23, w^{2} - 3w - 8]$ $\phantom{-}\frac{1}{2}e^{2} - \frac{1}{2}e - 5$
23 $[23, 23, w - 1]$ $\phantom{-}\frac{1}{2}e^{2} - \frac{1}{2}e - 5$
27 $[27, 3, 3]$ $-1$
29 $[29, 29, w^{2} - 2w - 5]$ $\phantom{-}\frac{1}{2}e^{2} - e - \frac{17}{2}$
29 $[29, 29, w^{2} - 3w - 10]$ $\phantom{-}\frac{1}{2}e^{2} - e - \frac{17}{2}$
29 $[29, 29, w - 3]$ $\phantom{-}\frac{1}{2}e^{2} - e - \frac{17}{2}$
31 $[31, 31, w^{2} - 2w - 6]$ $\phantom{-}\frac{1}{2}e^{2} - e + \frac{1}{2}$
31 $[31, 31, -w^{2} + 3w + 9]$ $\phantom{-}\frac{1}{2}e^{2} - e + \frac{1}{2}$
31 $[31, 31, w - 2]$ $\phantom{-}\frac{1}{2}e^{2} - e + \frac{1}{2}$
37 $[37, 37, -w^{2} + 4w + 7]$ $-3e + 2$
43 $[43, 43, 2w^{2} - 6w - 13]$ $-\frac{3}{4}e^{2} + \frac{5}{2}e + \frac{21}{4}$
43 $[43, 43, 2w^{2} - 4w - 17]$ $-\frac{3}{4}e^{2} + \frac{5}{2}e + \frac{21}{4}$
43 $[43, 43, w^{2} - 2w - 12]$ $-\frac{3}{4}e^{2} + \frac{5}{2}e + \frac{21}{4}$
47 $[47, 47, w^{2} - 4w - 4]$ $-\frac{5}{4}e^{2} + 3e + \frac{41}{4}$
47 $[47, 47, w^{2} - w - 5]$ $-\frac{5}{4}e^{2} + 3e + \frac{41}{4}$
Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$27$ $[27, 3, 3]$ $1$